The seminar meets regularly on Wednesdays at 4pm in Eckhart 202. We also have special seminars during other days. To subscribe or unsubscribe the email list, you may either go to Camp/PDE email list or contact Cornelia Mihaila.
TBA
Clouds and precipitation are among the most challenging aspects of weather and climate prediction. A related challenge is that our understanding of atmospheric dynamics is largely based on 'dry' dynamics without consideration of water vapor and phase changes. New mathematical and physical insight are needed. In this direction, in this talk, we investigate the PDEs of weather prediction models, or simplified versions of them, which essentially describe atmospheric fluid dynamics with phase changes of water. In an asymptotic limit, we derive precipitating quasi-geostrophic (PQG) equations that move beyond the traditional 'dry' QG equations. The PQG equations include interesting Heaviside nonlinearities due to phase changes of water. As illustrations and example applications, we will also describe new viewpoints of basic features such as fronts and conserved energies.
We prove new comparison principles for viscosity solutions of non-linear integro-differential equations. The operators to which the method applies include but are not limited to those of Levy-Ito type. The main idea is to use an optimal transport map to couple two different Levy measures, and use the resulting coupling in a doubling of variables argument. This is a joint work with Nestor Guillen and Andrzej Swiech.